Let v = 3i + 2j and w = 2i + 3j. sketch v, w, v + w, 2w, and v − w in the plane

Step-by-step explanation:

In the argand plane for plotting points of complex numbers we take i coefficient as x and j coefficient as y and plot as we plot regular points on the graph.

v=3i+2j

Point is (3,2) A

w =2i+3j , Point is (2,3) B

v+w = 5i +5j Point is (5,5) C

2w = 4i+6j , point is (4,6)

v-w = i-j Point (1,-1)

Please find enclosed the above points plotted on the graph.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional